电动力绳系周期解求解及稳定性控制

摘要

The dynamic equations of EDT (Electrodynamic Tether)attitude libration are nonlinear and EDT opera-tion in orbit is affected by attitude libration states.Governing equations of EDT in an inclined circular orbit are de-rived based on dumbbell tether model and a dipole model for the Earth magnetic field.The procedure of using a nu-meric method combining perturbation method and stationary point iteration method to seek periodic solutions for nonlinear equations is presented and a corresponding method of determining the stability of periodic solution is put forward.A feedback control strategy is presented to stabilize non-stable periodic solutions.The portraits of periodic solutions for attitude libration are got through numerical simulation.This validates the periodic solution algorithm and verifies that the control law stabilizes the unstable periodic solutions.%电动力绳系姿态摆动动力学方程具有非线性特点，且姿态摆动状态直接影响着空间任务能否正常进行。首先，基于哑铃模型及偶极子地磁场模型假设，推导了在倾斜圆轨道上运行的电动力绳系姿态动力学方程。其次，给出了利用摄动法和不动点迭代法相互配合的数值方法求解该非线性方程周期解的过程及解的稳定性判断准则，并针对不稳定周期解提出了相应的稳定性控制策略。最后，通过数值仿真分析，得到了姿态摆动运动的周期解图像，验证了周期解求解算法的有效性，并对不稳定周期解实现了稳定性控制。